Network Analyzer and Network Analysis

Transcription

1 Part I Network Analyzer and Network Analysis 1 Objectives Upon completion of the lab experiment, the student will become familiar with the following topics: 1. Get acquainted with the major elements of the Network Analyzer. 2. Using the Network Analyzer to characterize two port passive elements, such as lters, coaxial cable etc. 3. Understand the meaning of S parameter measurement using a Network Analyzer. 4. Get familiar with the various Re ection and Transmission parameters such as return loss, re ection coe cient, time delay, and group delay. 5. Understand the basic properties of passive networks, such as lossless, reciprocal etc. 6. Understand the concept of various calibration of the Network Analyzer. 2 Prelab Exercise 1. De ne the following parameters: return loss, lossless network, unitary matrix, delay, phase delay, group delay. 2. An electromagnetic wave s (t) = t pass through 10m coaxial cable, the velocity of the electromagnetic wave is 2=3c; (a) Find the dielectric constant of the coaxial cable. (b) Calculate the time delay of the cable. 1

2 (c) Calculate the phase delay of the cable.. 3. Two set of measurement were taken, at frequencies f 1 and f 2, can you decide if either is dispersive? 6 Frequency jh (f)j (db) H (f) (deg) f f f f Frequency jh (f)j (db) H (f) (deg) f f f f The measurement results of 4 ports network, directional coupler is given by the scattering matrix, p2 1 p2 1 j 0 p1 1 [S] = B p2 j p 1 2 j 0 0 p2 C A 1 0 p2 1 j p2 0 determine whether the network is matched, reciprocal, and lossless? 2.1 References [1] D.M. Pozar, Microwave engineering, 3rd edition, 2005 John-Wiley&Sons. 3 Background Theory 3.1 Transmission Line Summary Transmission line theory apply, when the dimension of the line is in the same order of magnitude as the wavelength transmitted through. In this case if the load impedance Z L 6= Z 0 ; part of the incident wave is re ected back to 2

3 the source. The amount of re ection is de ned by the quantity = V REF LECT = Z L Z 0 V INCID Z L + Z 0 (1) 1 < < 1 = j j 0 < < 1 Z 0 = 50 (2) Z L = 25 (3) Z 0 = 50I Z L = 25I V inc V ref Fig. 1 Transmission line, having characteristic impedance of 50; terminated with 25 In our application we need to deals with wide dynamic value of re ection coe cient, therefore we de ne a new logarithmic name of re ection coe - cient, which is called Return loss, and de ned by Re turn Loss (db) 20 log (4) Re ection coe cient has complex value, while Z L or Z 0 have complex value. Another important re ection quantity is Standing Wave Ratio (SWR), which related to re ection coe cient magnitude by SW R = < SW R < 1 (5) 3

4 3.2 Propagation Constant Propagation constant is a complex quantity, which describe the e ect of the transmission line, on the propagate wave. The linear e ects describe by the real part, the attenuation (neper=meter) ; and imaginary part (radian=meter), phase constant, or wave number and de ned by 3.3 Network Analyzer = + j (6) = 2 RF switch Incident power RF Source Splitter Splitter Directional Coupler Ref R 1 Reflected Transmited LO Ref R 2 Reflected Transmited Directional Coupler Receiver A B Receiver Test port 1 DUT 3 db Attenuator Fig. 2 Major elements of Network Analyzer Test port Signal Source The signal source supplies the stimulus for our stimulus-response test system. We can either sweep the frequency of the source or sweep its power 4

5 level. Modern source are synthesized sources, providing excellent frequency resolution and stability Signal Separation Devices- Splitter and Directional Coupler. The next major area is the signal separation block. The hardware used for this function is generally called the test set. There are two functions that our signal-separation hardware must provide. The rst is to measure a portion of the incident signal to provide a reference for ratioing. This can be done with splitters or directional couplers. Splitters are usually resistive. They are non-directional devices and can be very broadband. The trade-o is that they usually have 6 db or more of loss in each arm. Directional couplers have very low insertion loss (through the main arm) and good isolation and directivity. The second function of the signal splitting hardware is to separate the incident (forward) and re ected (reverse) traveling waves at the input of our DUT Receiver The receiver provides the means of converting and detecting the RF or microwave signals to a lower IF. The tuned receivers provide a narrowband-pass Intermediate-Frequency (IF ) lter to reject spurious signals and minimized the noise oor of the receiver. The vector measurement systems have the high dynamic range, and immunity to harmonic and spurious responses, they can measure phase relationships of input signals and provide the ability to make complex calibrations that lead to more accurate measurements. 4 Input Impedance Z in and Characteristic Impedance Z 0 According to the transmission line theory input impedance of a lossless transmission line terminated by load Z L ; expressed by Z in = Z 0 Z L + jz 0 tan l Z 0 + jz L tan l where Z 0 is characteristic impedance and l is the line length: 5 (7)

6 l Z in Z 0 β Z L Fig-3 Input impedance of transmission line with arbitrary load Z L : If Z L = 0 or,z L = 1 equation [7] reduce to using equation [8] we may rewrite Z in(sc) = jz 0 tan l (8) Z in(oc) = Z 0 j cot l Z 0 = p Z in(sc) Z in(oc) (9) The idea of equation [9] is a useful way to measure characteristic impedance, of DUT, by measuring Z in(sc) and Z in(oc) of the DUT. 5 The De nition of S-Parameter Scatter Parameters, also called S-parameters. Like the H,Y,Z or ABCD parameter, they describe the performance of linear n-ports device completely. They relate to the traveling waves that are scattered or re ected when a network is inserted into a transmission line of a certain characteristic impedance Z L. Incient wave a 1 S 21 LTI 1 S 11 S 22 2 Network S 12 Incient wave a 2 Reflected wave b 1 Reflected wave b 2 6

7 Fig. 4 S parameter ow graph S-parameters are important in microwave design because they are easier to measure and to work with at high frequencies than other kinds of two port parameters. However, it must kept in mind that -like all other two port parameters, S-parameters apply to LTI network, I.e. they represent the linear behavior of the two ports. S-parameters are de ned as: b 1 = S 11 a 1 + S 12 a 2 (10) b 2 = S 21 a 1 + S 22 a 2 a i -E ective value (rms) of the incident wave traveling towards the i two port gate. th b i -E ective value (rms) of the wave re ected back from the i port gate. th two The signal ow graph gives the situation for the S-parameter interpretation in voltages: Looking at the S parameter coe cients individually, we have S 11 = 1 = b 1 = V re ected at port 1 a 1 V forward port 1 (11) a2 =0 S 12 = b 1 = V out of port 1 a 2 V forward port 2 a1 =0 S 21 = b 2 = V out of port 2 a 1 V forward port 1 a2 =0 S 22 = 2 = b 2 = V out of port 2 a 2 V forward port 2 a1 =0 S 11 and S 21 are determined by measuring the magnitude and phase of the incident, re ected and transmitted signals when the output is terminated in a perfect Z 0 load. This condition guarantees that a 2 is zero. S 11 is equivalent to the input complex re ection coe cient or impedance of the DUT, and S 21 is the forward complex transmission coe cient. 7

8 Likewise, by placing the source at port 2 and terminating port 1 in a perfect load (making a a 1 zero), S 22 and S 12 measurements can be made. S 22 is equivalent to the output complex re ection coe cient or output impedance of the DUT, and S 12 is the reverse complex transmission coe cient. 5.1 Properties of Network Matched network S 11 = S 22 = 0 A reciprocal network -S-parameter matrix is symmetric about its diagonal or equal to its transpose, S ij = S ji Lossless network the power incident on the network must be equal nx nx to the power re ected, or ja i j 2 = jb i j 2 ; or in in mathematics, a i=1 unitary matrix is an n by n complex matrix U satisfying the condition U + U = UU + = I n : 5.2 Nondispersive (Distortionless) Transmission In communication systems, a nondispersive channel, or low distortion is often desired. This implies that the channel output y(t) is just proportional to a time delayed version of the input x (t) i=1 y(t) = Ax(t T d ) (12) R x(t) C y(t) Fig-5 An arbitrary network where A is the gain (which may be less than unity) and T d is the delay. 8

9 5.2.1 Delay and Phase Delay For a non-dispersive DUT, e.g. a coaxial cable, phase (f) is a linear function of frequency: (f) = 360 ft d (13) where T d is the delay time of the cable which is the time that the electromagnetic wave pass through the cable. Phase delay is directly related to its mechanical length l via the permittivity r of the dielectric material within the cable, therefore the time delay is de ned by T d = lp r c (14) The corresponding requirement in the frequency domain is obtained by taking the Fourier transform of both sides of Eq. (12). Y (f) = AX(f) exp ( j2ft d ) (15) Thus, for distortionless transmission, we require that the transfer function of the channel be given by H(f) = Y (f) X(f) = A exp ( j2jft d) (16) which implies that, distortionless network, must be satis ed two requirements: 1. The amplitude response versus frequency must be at. That is H(f) = constamt = A (17) 2. The phase response is a linear function of frequency. That is (f) = 6 H(f) = 2fT d (18) When the rst condition is satis ed, there is no amplitude distortion. When the second condition is satis ed, there is no phase distortion. For non dispersive transmission, both conditions must be satis ed. 9

10 By Eq:(14), it is required that T d (f) = constant for non dispersive transmission. If T d (f) is not constant, there is phase distortion. The linearity of phase versus frequency is characterized by group delay which de ned as (f) 1 d (f) 360 df (19) That is the negative of the rate of change of phase ( which measure in degree) with frequency. The quantity has the dimension of time, but the question is; what time does it represent? Many textbooks follow the de nition of group delay with a discussion of an ideal element that delays a signal by time T d : 10

11 Part II Experiment Procedure 6 Required Equipment 1. RF Network Analyzer E5062A 2. Type N calibir4ation kit Agilent E 3. Band Pass Filter Mini - Circuit BBP MHz 4. Terminator 50 NTRM Agilent ADS simulation software 6.1 Simulating a Network Analyzer Measurement. In this part of the experiment we simulate the re ection and transmission measurement of a 10.7MHz BPF. 1. Simulate a re ection and transmission measurement (S 11 and S 21 ) ; of a 10.7 MHz BPF, using ADS software. The de nition of the lter parameter is ginen in Fig. 10. Fig. 9 simulation of re ection and transmission of 10.7MHz BPF 11

12 Astop 0-3dB point Passband ripple BW pass -10 db(s(2,1)) -30 BWstop freq, MHz Fig.-10 De nition of an Elliptic BPF 2. Draw a graph of S 11 (magnitude), S 11 (db), S 21 and and Fill Table-1 according to simulation results. BPF Electrical Transmission Results Passband IL Stopband Center Freq. BW(-3dB) IL > 20dB@Freq. IL@7.5 MHz IL@15 MHz Selectivity 20dB bandwidth 3dB bandwidth Re ection max j j 9 to 12MHz; max RL 9 to 12MHz j RL@15MHz Table-1 12

13 7 Getting Started With Network Analyzer 7.1 Front Panel View Refer to Fig.-6: 1. Standby Switch Allows the switch between power-on (j) and standby mode (Ö) on the E5061A/E5062A. 2. LCD Screen Displays measurement traces, instrument setting conditions, and menu bars. 3. ACTIVE CH/TRACE Block A group of keys used for selecting the active channel and an active trace. 4. RESPONSE Block A group of keys used for the selection of a measurement parameters/data formats, displaying, calibration, etc. 5. STIMULUS Block A group of keys used for specifying the setup for signal sources, trigger, etc. 13

14 RF OUT RF IN NAVIGATION Block Fig-6 Front panel tour A group of keys used for the movement/selection of the focus in menu bars/soft-key menu bar/dialog boxes and for manipulating markers. 7. ENTRY Block A group of keys used for entering numeric data on the E5061A/E5062A settings. 8. INSTR STATE Block A group of keys used for specifying the setup for controlling and managing the E5061A/E5062A such as executing printing measurement results, and presetting (initializing) the E5061A/E5062A. 9. MKR/ANALYSIS Block A group of keys used for analyzing measurement results through markers, the limit test function, etc. 10. Test Port 14

15 While the signal is being output from a test port, the yellow LED above the test port lights up. The connector type adopted is the 50 -based N-type (female) connector. 11. Front USB Port Used to connect a printer, or an ECal module compatible with the USB (Universal Serial Bus). Using a USB port allows the accessories to be connected after the E5061A/E5062A has been powered on. 12. Ground Terminal Connected to the chassis of the E5061A/E5062A. You can connect a banana type plug to this terminal 8 Re ection Measurement 8.1 Preparation to Re ection Measurements, Re ection Calibration When you require best possible accuracy, or you need to add an adaptor or cable between the DUT and the test port, it is strongly recommended to perform a proper calibration. 1. Press Preset and OK. 2. Press CAL key and then choose Calibrate, 1- Port Cal 3. Connect an open to the re ection port and press Open(f) (see gure 7). 4. Connect a short to the re ection port and press Short(f). 5. Connect a load to the re ection port and press Load and in the end press Done. 6. You use 3 standards, (open short and 50 load); could you determine Z 0 using two standards? Prove your answer using proper equation. 7. Disconnect the load (50 termination) and return all the standards devices carefully to their box. 15

16 RF OUT RF IN 50Ω Load open short Fig. 7 Calibration for Re ection measurement 8.2 Preparation to Re ection Measurement, Setting Signal Source S. parameters is a ratioing measurement. If your device is sensitive to the incident power, you can increase or decrease the incident power. 1. Connect a 10.7MHz BPF to the Network Analyzer as shown in Figure Press the Preset key situated at INSTR STATE Block. 3. Press the Measr key situated at Response Block, and choose S 11 from the soft menu, and press Enter. 4. Press the Scale key, and choose Autoscale from the soft menu. 5. At the STIMULUS Block press: Start key and insert 5 MHz by pressing 5 M=, press Stop key and insert 20 MHz. 16

17 RF OUT RF IN 10.7 MHz BPF 50Ω Load Fig. 8 Basic re ection neasurement 6. By default the power level of the Network Analyzer is 0 dbm (1mw). If necessary you can change the power by pressing Sweep Setup keys and then choose Power option and set power level to 3dBm, by pressing 3 1 keys. 9 Re ection Measurement of a BPF Under Re ection measurement you can measure: re ection coe cient magnitude and phase, return loss, SWR, and impedance of a DUT. 1. Press the Preset key situated at INSTR STATE Block. 2. Press the Measr key situated at Response Block, and choose S 11 from the soft menu, and press Enter. 3. Press the Scale key, and choose Autoscale from the soft menu. 4. Press Freq, then Start 1 MHz and Stop 25 MHz, Scale, Autoscale, return loss (S 11 ; re ection coe cient j j in db) as a function of frequency is displayed). Save the data of S 11 and S 22 on magnetic media, Excell and image format. 17

18 5. Press Format, Lin Mag, to get the absolute value of re ection coe cient as a function of frequency is displayed ( = j j):set marker 1 to 10.7MHz, and marker 2 to 25MHz. Explain what happen to the incident power at that frequencies? Save the data on magnetic media. 6. Press Format Polar, to get polar plot of the re ection coe cient, could you explain where ; 6 and frequency is displayed?.save the data on magnetic media. 7. Fill Table-2. Freq(MHz). RL(data) RL(meas.) j j(meas.) P inc (mw) P ref = j j 2 P inc Stop band x x x x x (center) Table Standing Wave Ratio and Impedance 1. Press Format, and SWR. The SWR as a function of frequency is displayed.save the data on magnetic media. 2. Press Format and Smith Chart for getting a display of the real and imaginary values of the impedance as function of frequency. Set the start frequency to 7 MHz and stop frequency 20 MHz, verify that the impedance of the lter is about 50 in the pass Band (8:5 to 12:5MHz).Save the data on magnetic media. 3. Fill Table-3 Stop band<7.5mhz SWR(Data ) SWR(measured) 16 Pass band(9.5 to 11.5MHz) SWR(Data ) SWR(measured) < 1:7 Table-3 18

19 10 Make a Transmission Measurement of a BPF In this part of the experiment you measure insertion loss (attenuation, S 21 ) of a BPF as a function of frequency using Transmission measurement Preparation to transmission Measurement- Response Calibration In this part of the experiment we eliminate the errors due to frequency response of the external cable connected between port-1 and port-2 of the Network Analyzer. 1. Connect a coax cable to the network between RF out port and RF in port (see Fig. 10 dashed line). 2. Set the frequencies range, 300kHz to 1GHz. 3. Press Preset, Ok and Measurement, S Press CAL, calibrate, Response(Thru), Thru, Done Transmission Measurement of an Elliptic BPF. In this part you measure the insertion loss of the BPF, at the pass band and at the stop band. 1. Disconnect the coaxial cable and connect the BPF to the re ection port of the Network Analyzer, as indicated in Figure Set the frequency range to start frequency 5MHz stop frequency 20MHz, transmission coe cient measurement in db is displayed (S 21 ). 3. Press Scale, Autoscale. and Save the data of S 21 and S 12 on your media, Excell, and image format. 4. Press Marker Search, Max verify that the center frequency of the lter is about 10.7 MHz and ll Table-4. 19

20 5. Set the marker to 9.5 MHz and 11.5 MHz by pressing Marker 9.5 MHz, and then 11.5 MHz, verify that the insertion loss is less than 1.5 db. Pass Band measurements Center Freq. Passband(IL<1.5dB) Typ. bandwidth(-3db) Bandwidth(-20dB) (10:7M Hz) (9:5 to 11:5M Hz) (8:9 12:7M Hz) (7:8 14:4) Selectivity 20dB MHz MHz Freq 3dB (1:7) ( 1dB) ( 1dB) Stop Band IL@7.5 MHz IL@15 MHz IL@0.6 MHz Freq.@-20dB (30dB) (30dB) (60dB) (7:6&14:4) Table-4 6. Measure the phase of the lter in the pass band ( MHz), explain if the phase is linear in the passband? RF OUT RF IN 10.7 MHz BPF Response calibration Filter transmission measurement Fig. 10 Response calibration and transmission measurement of a BPF. 20

21 11 Delay and Phase Delay In this part of the experiment you simulate and measure the delay (group delay), and phase delay of a coaxial cable Group Delay, and Phase Simulation 1. Simulate a 5m coaxial cable as indicated in Fig Allow group delay simulation by double click on S PARAMETER, then click on parameters, and select Group delay. S-PARAMETERS S_Param SP1 Start=1.0 MHz Stop=200 MHz Step=10.0 khz P_1Tone PORT1 Num=1 Z=50 Ohm P=polar(dbmtow(0),0) Freq=1 GHz COAX TL1 Di=0.9 mm Do=3.275 mm L=5000 mm Er=2.1 TanD=0.002 Rho=1 Term Term2 Num=2 Z=50 Ohm Fig-11 Group delav and phase delay simulation 3. Plot a graph of delay S 21 (group delay) as a function of frequency, according to the graph explain if the cable is dispersive element? 4. Calculate, phase constant ;and phase delay at 100MHz. Plot a graph of S 21 phase and nd the phase delay at 100 MHz, you can verify your result by changing the graph expression to plot_vs(unwrap(phase(s(2,1))), freq). 5. Replace the coaxial cable with elliptic band pass lter as indicated in Fig. 12 and simulate the group delay of the lter. 21

22 S-PARAMETERS S_Param SP1 Start=1.0 MHz Stop=20 MHz Step=10.0 khz P_1Tone PORT1 Num=1 Z=50 Ohm P=polar(dbmtow(0),0) Freq=1 GHz BPF_Elliptic BPF1 Fcenter=10.7 MHz BWpass=3.8 MHz Ripple=1 db BWstop=6.8 MHz Astop=20 db Term Term2 Num=2 Z=50 Ohm FIG. 12 group delay of elliptic BPF 6. Plot a graph of S 21 group delay and S 21 phase, according to the graphs, explain if the lter can be used for baseband digital communication (linear phase versus frequency is important) Group Delay and Phase Delay Measurement 1. Connect a 5m long, coaxial cable to the Network Analyzer as indicated in Fig. 10 dashed line. 2. Calculate the group delay (time delay), assume r = 2:29: 3. Calculate the phase shift of the cable, at 100MHz. 4. Under transmission measurement, frequency range 300kHz to 1GHz, measure the group delay of the cable (under Format, Group Delay). according to your measurement explain if the cable is dispersive element? Compare your measurement to the calculation. 5. Measure the phase shift of the cable, and compare to the calculation. 6. Replace the cable with BPF and measure the group delay of the lter, and compare to the simulation result. 22

23 12 Final Report Using your data and mathematics software, or spreadsheet answer the following Questions. 1. Attached the graphs that you save, and answer the question of the text Lab. 2. Draw a graph of return loss (S 11 in db)based on measurement as a function of frequency of the Elliptic lter. Calculate the worst SWR of the cable. in the passband (9.5 to 11.5 MHz). 3. Use the data of the lter to ll the following S parametrsmatrices, determine S11 S = 12 S 21 S 22 S11 S Hz = 12 S 21 S 22 (a) If the lter is matched, reciprocal, and lossless at center frequency. (b) If the lter is matched, reciprocal, and lossless at 8.5MHz. 23